Figure REF  (a) shows the overview of the proposed joint training of SE frontend and ASR backend. We additionally use the SNRi prediction network which predicts a target SNRi \(\lambda \)  which minimizes the ASR loss. The architecture of the SNRi prediction network used in this study is shown in Fig. REF  (b). First, log-mel-filterbank outputs are passed to the first dense layer for calculating bottleneck features, and Conformer-blocks [1]} are applied to the bottleneck feature. Then, the second dense layer and the sigmoid function are applied to the Conformer output to change the feature dimension to 1. Finally, a scaling operation to restrict the predicted target SNRi to \([\lambda _{\min },\lambda _{\max }]\)  is applied, and target SNRi \(\lambda \)  is estimated by taking average of it over time-frames. Here \(\lambda _{\min }\)  and \(\lambda _{\max }\)  are hyperparameters that represents the minimum and maximum values of target SNRi.
